2.2. Powder XRD Analysis
Powder XRD studies revealed a clear correlation between the crystal structure of the synthesized polycrystalline M+(Yb0.99Tm0.005Ho0.005)(MoO4)2 samples and the nature of the alkali cation.
All diffraction peaks observed for the Li(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 specimen (
Figure 3a) correspond to a pure phase crystallizing in the tetragonal space group
I 4 (PCD #1321581). Thus, Li(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 demonstrates tetragonal symmetry characteristic of scheelite-type structures, although with some distortion relative to the scheelite space group
I4
1/
a. The experimental PXRD pattern obtained in this study and the observed diffraction peaks match well the calculated pattern for the
I 4 structure reported by Volkov et al. [
19]. Volkov et al. systematically refined the structure of the archetypal compound LiYb(MoO
4)
2 using three tetragonal space groups commonly considered for double molybdates and tungstates:
I4
1,
I4
1/
a, and
I 4. Their analysis demonstrated that only the non-centrosymmetric
I 4 space group adequately described the atomic positions, particularly the partial occupancy of Li
+ and Yb
3+ ions over two distinct crystallographic sites.
PXRD analysis of the Na(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 sample confirms that the main phase corresponds to the target double molybdate. The major diffraction maxima are readily indexed to the tetragonal structure of NaLu(MoO
4)
2 (sp. gr.
I4
1/
a, PCD #1051174) (
Figure 3b). In addition, several weak reflections indicate the presence of a minor Yb
2MoO
6 impurity crystalline phase, along with a few unidentified peaks observed at 2
θ = 25.83°, and 26.19° (insert on
Figure 3b).
The solid-state reaction in the ternary Cs
2O–Yb
2O
3–MoO
3 system upon high-temperature annealing leads to the formation of the double molybdate CsYb(MoO
4)
2 (sp. gr.
Pccm, PCD #1610499) (
Figure 3c). However, the diffraction pattern of the synthesized product was not single-phase: alongside the main reflections of the target phase, additional diffraction maxima corresponding to the co-crystallizing phase (Yb
0.99Tm
0.005Ho
0.005)
2(MoO
4)
3 were detected, as well as an unidentified reflection at 2
θ = 8.2°. The presence of these impurities indicates that the selected synthesis conditions do not fully complete the solid-state interaction, or that the initial Cs
2O/Yb
2O
3 ratio deviates from the stoichiometric one. The low-angle unidentified reflection suggests possible layered or superstructural ordering, which merits further investigation via electron microscopy or synchrotron XRD.
In the K
2O–
R2O
3–MoO
3 system, the primary crystalline phase was identified as K(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2, which adopts the orthorhombic space group
Pbcn (
Figure 4). This structure is characteristic of potassium rare-earth double molybdates containing heavy
R3+ cations [
3,
4,
20]. In addition to the main phase, several weak diffraction peaks were observed that could not be attributed to K(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2. Based on their positions and relative intensities, these reflections are assigned to the palmierite-type phase K
5Yb(MoO
4)
4, which is known to exist in three polymorphic modifications: the low-temperature
γ-phase (monoclinic, space group
C2/
c, ordered cation distribution), the intermediate
β-phase (incommensurately modulated structure), and the high-temperature
α-phase (trigonal, space group
R 3
m, statistical cation distribution) [
21]. The low intensity of the additional reflections indicates that K
5(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
4 is present only as a minor impurity phase. To interpret these extra reflections and to clarify the origin of the unusual thermal behavior deviating from that of pure KYb(MoO
4)
2 (see
Section 2.3), a Le Bail fitting was performed (
Figure 4). The crystal structures of KYb(MoO
4)
2 (PCD #1342365) and K
5Yb(MoO
4)
4 (PCD #1003278) were used as initial structural models. The refinement converged with the reliability factors shown in
Figure 4, confirming good agreement between the observed and calculated profiles. The obtained unit-cell parameters for the main phase are
a = 5.04110(13) Å,
b = 18.2856(3) Å, and
c = 7.86414(16) Å. The presence of a secondary phase identified as K
5Yb(MoO
4)
4 with the lattice parameters
a = 14.8787(12) Å,
b = 12.5213(12) Å,
c = 10.3165(8) Å, and
β = 113.600(7)° was also confirmed (green and orange vertical marks in
Figure 4 correspond to Bragg reflections of K(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 and K
5(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
4, respectively).
According to PXRD data, the phase composition in the Rb
2O–Yb
2O
3–MoO
3 system at the stoichiometry corresponding to Rb(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 is characterized by the presence of at least two phases. The main phase is a rubidium-rich compound of the Rb
5(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
4 composition, isostructural to Rb
5Er(MoO
4)
4, crystallizing in the monoclinic system with space group
P2/c [
22]. The target phase Rb(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 is present in substantially smaller amount. Preliminary X-ray phase analysis suggests two possible variants for Rb(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2: orthorhombic
Pbcn and monoclinic
P2/
c. In order to clarify probable Rb(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 phase and to confirm the phase composition, a Le Bail analysis was performed. Two models of phase composition were considered: (
i) K
5Er(MoO
4)
4 (PCD #1003278) + KYb(MoO
4)
2 (PCD #1342365, sp. gr.
Pbcn) and (
ii) K
5Er(MoO
4)
4 (PCD #1003278) + CsGd(MoO
4)
2 (PCD #1141740, sp. gr.
P2/
c).
The obtained results unambiguously confirm the presence of the Rb
5(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
4 phase in the sample. This structural type is well established for the isostructural potassium analogue K(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2, whose single-crystal structure was determined in the
Pbcn space group [
20]. Both models demonstrate close agreement factors, indicating that the refinement does not allow definitive assignment between the two possible space groups for the Rb(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
4 phase. However, the model with the
P2/
c space group for Rb(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
4 shows slightly better
Rp and
Rwp values, which may indicate a monoclinic distortion of the second phase structure (
Figure 5).
The formation of the Rb
5(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
4 compound at the stoichiometry corresponding to Rb(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 can be attributed to several factors. Compounds of the composition
M5R3+(MoO
4)
4 (
M+ = K, Rb) are characteristic phases in the
M2MoO
4–
R2(MoO
4)
3 systems, stable in the subsolidus region [
23,
24]. The high rubidium content in this phase (Rb:Yb ratio = 5:1) explains its predominant formation under the employed synthesis conditions. Additionally, kinetic factors may favor the formation of this phase at the initial stages of solid-state interaction, especially if the synthesis temperature is insufficient for complete reaction or if local stoichiometric fluctuations occur due to MoO
3 volatility.
2.3. Thermal Behavior
DSC studies of
M+(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 (compounds were conducted in the temperature range of 50–1200 °C (
Figure 6a–e). The results revealed distinct patterns in their thermal behavior. To clarify the melting behavior, the
M+(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 samples were re-examined after thermal studies using X-ray diffraction technique.
The thermal behavior of Li(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2, as revealed by differential scanning calorimetry technique, shows that the compound melts congruently at approximately 935 °C (onset temperature, T
onset), with subsequent crystallization occurring at 893 °C upon cooling (
Figure 6a). The absence of additional peaks on the thermal curves and the full reversibility of the melting/crystallization process, confirmed by the good agreement between the PXRD patterns before and after the DSC run (see insert on
Figure 6a), indicate that LiYb(MoO
4)
2 is stable as a single phase up to its melting point and undergoes no polymorphic transitions or decomposition in the solid state.
Regarding the melting behavior, DSC data, obtained in this study, clearly demonstrate a single, reversible melting event. However, the literature contains inconsistent findings on the melting nature of LiYb(MoO
4)
2 compounds. Klevtsov and Kozeeva initially reported the melting of LiYb(MoO
4)
2 at ~900 °C [
1], but the nature (congruent vs. incongruent) was not explicitly stated. In contrast, a later study by Volkov et al. [
19], concluded that LiYb(MoO
4)
2 melts incongruently at 912 °C, decomposing to Yb
2(MoO
4)
3 and a liquid phase. Our results, which show complete reversibility and no decomposition products after melting and recrystallization, strongly suggest congruent melting of Li(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 at ~935 °C. The observed inconsistency may arise from differences in synthesis conditions, heating rates, or the specific starting compositions used in the flux growth experiments by Volkov et al., where higher concentrations of LiYb(MoO
4)
2 in the melt might have led to decomposition. Our data, obtained from a pure, well-characterized polycrystalline sample, support the conclusion that the compound is stable as a single phase up to its melting point.
The thermal behavior of the synthesized Na(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 sample, as revealed by DSC studies, demonstrates a sequence of melting and recrystallization events that aligns with the established polymorphism of double alkali-rare-earth molybdates (
Figure 6b). According to the comprehensive review by Klevtsov and Klevtsova [
3], the double molybdates and tungstates
M+R3+(
EO
4)
2 represent a system of structural types related by morphotropic and polymorphic phase transformations. Within this class, sodium compounds Na
R3+(
EO
4)
2 typically crystallize in the tetragonal scheelite-type structure (sp. gr.
I4
1/
a) and are often reported as non-polymorphic, particularly for NaY(MoO
4)
2 which does not possess solid-phase polymorph transitions [
25]. However, recent studies have revealed that polymorphism can be induced under specific conditions; for instance, NaGd(MoO
4)
2 has been shown to exhibit a fergusonite-type monoclinic polymorph that undergoes an irreversible phase transition to the scheelite structure at approximately 813 K [
26].
On the heating curve, a single sharp endothermic peak with T
onset of 1076 °C is observed, assigned to the melting of the Na(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 phase. Although some literature sources report incongruent melting for certain heavy rare-earth sodium double molybdates, the observation of only one endothermic event on heating suggests that the primary phase melts without prior decomposition. Upon cooling, two distinct exothermic events are recorded: a low-intensity exotherm at 1115 °C and a well-defined, intense exotherm at 1067 °C. The intense peak at T
onset = 1067 °C is attributed to the crystallization of the Na(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 melt, which is the reverse of the melting process. The smaller exotherm at 1115 °C is assigned to a high-temperature polymorphic phase transition—a subtle cation-ordering phenomenon often observed in scheelite-type structures. As noted by Klevtsov and Klevtsova, phase transformations in these compounds frequently exhibit weak thermal effects and may not be detectable by conventional experimental methods, especially when the high-temperature modification is stabilized or quenched [
2].
Crucially, the post-DSC XRD analysis shows that the diffraction pattern of the product after thermal cycling is identical to that of the as-synthesized sample. This finding unambiguously confirms that the primary Na(Yb0.99Tm0.005Ho0.005)(MoO4)2 phase is fully recovered after melting and subsequent cooling, with no evidence of decomposition into secondary phases such as Yb2MoO6 or other reaction products. This observation is consistent with congruent melting behavior for the main phase. The presence of the minor Yb2MoO6 impurity phase, already detected in the as-synthesized material, remains unchanged after the thermal cycle, confirming that it is a persistent secondary phase originating from the synthesis and not a product of melt decomposition.
The heating curve revealed two distinct endothermic peaks with T
onset = 905 °C and 998 °C (
Figure 6c). Upon cooling, two exothermic peaks were observed at T
onset = 876 °C and 963 °C. The thermal effects are fully reproducible over several consecutive cycles.
To verify the reversibility of the observed thermal events and to exclude any decomposition or irreversible phase changes, PXRD patterns were recorded both before (as-synthesized) and after the DSC measurements. As shown in the inset to
Figure 6c, the diffraction patterns are identical within experimental error. This result unambiguously demonstrates that: (
i) no permanent decomposition or volatilization occurs during the thermal cycle; (
ii) all thermal events in the investigated temperature range are fully reversible; (
iii) no additional phases are formed upon melting and recrystallization.
The comparison of the PXRD patterns confirms that the main phase K(Yb0.99Tm0.005Ho0.005)(MoO4)2 melts congruently and recrystallizes into the same phase, while the minor K5(Yb0.99Tm0.005Ho0.005)(MoO4)4 phase undergoes only reversible structural transitions without decomposition.
The endothermic peak at 998 °C on heating and the corresponding exothermic peak at 963 °C on cooling are assigned to the congruent melting and solidification of the main K(Yb0.99Tm0.005Ho0.005)(MoO4)2 phase. The observed hysteresis of about 35 °C is typical for crystal-melt transitions of complex oxides.
The weaker endothermic peak at 905 °C (heating) and its exothermic counterpart at 876 °C (cooling) are attributed to a structural phase transition in the minor K
5(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
4 phase. According to [
21], this compound undergoes a reversible order–disorder transition from the low-temperature
γ-phase (monoclinic, sp. gr.
C2/
c) to the intermediate
β-phase upon heating, which is characterized by an incommensurately modulated structure. In pure K
5Yb(MoO
4)
4, the
γ →
β transition is observed in the range 938–968 °C upon heating [
21]. In the present study, the transition temperature
Ttr = 905 °C is slightly lower than that reported for the pure compound. This downward shift can be rationalized by: (
i) misfit strain imposed by the K(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 matrix on the embedded minor phase; (
ii) minor deviations in stoichiometry of the impurity phase (e.g., slight K/Yb non-stoichiometry), which are known to affect transition temperatures in palmierite-type phases; (
iii) different thermal history or heating/cooling rates compared to the literature data.
The reverse transition β → γ occurs at 876 K, giving a thermal hysteresis of Δ
T ≈ 29 °C, which is characteristic of first-order or strongly first-order-like transitions involving displacive mechanisms. This hysteresis is consistent with the first-order character of the γ ↔ β transition in the K
5Yb(MoO
4)
4 system, as reported by Morozov et al. [
21].
DSC studies of the sample in the Rb
2O–
R2O
3–MoO
3 system revealed two endothermic peaks upon heating with onset temperatures
Tonset = 786 and 1018 °C (
Figure 6d). Upon cooling, two exothermic peaks were observed with
Tonset = 1079 and 1018 °C.
The endothermic effect at 786 °C can be associated with a polymorphic transition in the Rb
5(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
4 phase. It is known that for the isostructural compound K
5Yb(MoO
4)
4, the existence of three polymorphic modifications (γ, β, and α) has been established, related by phase transitions not accompanied by significant rearrangement of the palmierite-type structure [
21]. Similar polymorphic behavior can be expected for Rb
5(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
4, which allows the endothermic effect at 786 °C to be interpreted as a transition between polymorphic modifications of this phase.
The endothermic effect at 1018 °C corresponds to the melting of the sample. This temperature is in good agreement with the general trend of increasing melting temperatures of rubidium double molybdates with heavy lanthanides as the ionic radius of
R3+ decreases [
3]. The exothermic peak at 1079 °C upon cooling exhibits significant thermal hysteresis (~61 °C) relative to the peak at 786 °C upon heating. Such behavior is characteristic of reconstructive phase transitions in double molybdates and tungstates, where the reverse transition requires significant supercooling and may be kinetically hindered [
2]. This is also consistent with data for K
5Yb(MoO
4)
4, where the transition between modifications also exhibits hysteresis [
21].
After the DSC study, the phase composition of the sample changed: the Rb(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 phase became predominant, while the Rb
5(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
4 content significantly decreased (see inset in
Figure 6d). This change unambiguously indicates that high-temperature treatment allows the system to approach thermodynamic equilibrium.
According to XRD data, the as-synthesized Cs(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 sample crystallizes in the orthorhombic modification (sp. gr.
Pccm) at room temperature. The DSC heating curve exhibits two endothermic peaks with onset temperatures 767 °C and 1139 °C (
Figure 6e). The first peak is attributed to a polymorphic transition from the
α-orthorhombic phase to the high-temperature
β-trigonal modification, which is in good agreement with the literature data for this family of compounds [
3]. The second peak at 1139 °C corresponds to melting; however, according to the available data [
1], the nature of fusion for CsYb(MoO
4)
2 has not yet been conclusively established. Upon subsequent cooling, only a single exothermic crystallization event is observed with
Tonset = 1067 °C, indicating supercooling of the melt. The reverse
β →
α polymorphic transition is not detected as a distinct thermal effect on the cooling curve, which is likely due to kinetic hindrance or a broad temperature range of the transformation. Importantly, the XRD patterns of the sample recorded before and after the thermal cycle are identical (except for the SiO
2 impurity originating from the agate mortar during grinding) and correspond to the initial orthorhombic
Pccm phase (
Figure 6e, inset). This finding demonstrates the full reversibility of the structural transformations within the investigated temperature range and indicates that the final room-temperature state is independent of the thermal history. Furthermore, the identity of the XRD patterns before and after melting–crystallization provides strong evidence that the melting of Cs(Yb
0.99Tm
0.005Ho
0.005)(MoO
4)
2 occurs congruently.